A teenage girl did a backwards “swan dive off the roof” of a 24-story Midtown building yesterday hours after a fight with her boyfriend, crashing with an explosive bang to the sidewalk as he watched helplessly from the street, cops and witnesses said.

Diana Chien, 19, took the plunge from 990 Sixth Ave., between 36th and 37th streets, around 5:50 p.m., horrifying a small group of passers-by who witnessed what police sources called a suicide.

“She was dangling over the edge for about five minutes” before jumping, one witness said. “It was the loudest boom ever.

“It sounded like two cars hitting each other at 30 mph.

“She bounced once.”

Chien, who lived nearby on Sixth Avenue, had gotten into an argument with her boyfriend earlier in the day, cops said. He tried to run to her aid when she hit the ground and had to be restrained by police officers.

Chien was rushed to Bellevue Hospital and died a few hours later, cops said.

Her dramatic plunge to the pavement was caught by Post photographer Scott Schwartz.

Schwartz said she had her back to the street when she leaped and stayed completely still all the way down.

“I saw one shoe go flying into the air after the impact,” Schwartz said. “I do recall her being barefoot.”

Schwartz said he assumed cops would talk the jumper off the ledge before she decided to take the leap.

“I’m a big fan of movies, and in the movies someone always gets that jumper to get back in,” Schwartz said. “Part of you thinks it’s not going to happen and then the unreal happens – she fell.”

Building resident Miki Feinberg said others have jumped from that address, including a woman who lived across the hall from her.

Geoff Gentile, who lives in a nearby Sixth Avenue building, said he was watching through a telescope and called cops to the scene.

“I saw her jump, but once she did, I looked away,” he said. “After that I went to my priest to pray for her.”

New Jersey resident Juilet Hoilett said she was in a nearby McDonald’s with her daughter when a man ran into the restaurant screaming, “Someone jumped!”

“I told my daughter to stay here and I ran outside because I feared that she might have hit my car,” Hoilett said.

“When I got out, I saw a woman and I just saw blood everywhere pouring out of her head. They checked for a pulse and then took her away.”